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TUTORIAL ON POLARIZATION RESISTANCE TECHNIQUE (Misnamed LINEAR POLARIZATION)

David C. Silverman


Table of Contents

Overview of Tutorial
Summary of Polarization Resistance Technique
Sources of Error
         Example (Nickel in Strong Acid)
Example (Low Corrosion Rate Environment)

Summary of Polarization Resistance Technique

Calculation of Corrosion Current

Excellent in-depth discussions are provided in F. Mansfeld, "The Polarization Resistance Technique for Measuring Corrosion Currents", in Advances in Corrosion Engineering and Technology (M. G. Fontana and R. H. Staehle, ed.), 6, ch. 3, Plenum Press, 1976 and more recently in J. R. Scully, "Polarization Resistance Method for Determination of Instantaneous Corrosion Rates", Corrosion, Vol.56, p. 199 (2000). Since such in-depth descriptions exist throughout the literature, only those portions pertinent to this tutorial are summarized below.

The overall technique requires the relationship between current measured versus voltage applied near the corrosion potential. Very often, the potential is scanned over a narrow voltage range centered on the corrosion potential, for example from -20 mV to +20 mV relative to the corrosion potential. The polarization resistance is determined from this curve as:

                                                                   (1)

where Rp is the polarization resistance determined from the slope (derivative) of the voltage (V) versus current density (i) curve at the corrosion potential. An example of a methodology for generating the potentiodynamic sweep in the vicinity of the corrosion potential is described very adequately in ASTM G59 "Standard Test Method for Conducting Potentiodynamic Polarization Resistance Measurements". This standard provides a test circuit and standard solution useful for determining if the electrochemical equipment is functioning properly.

The data are usually analyzed by assuming that the relationship between the current and voltage in the polarization curve is given by:

                                                                   (2)

where icorr is the corrosion current density, V is the applied (assumed to be actual) voltage, Vcorr is the corrosion potential, and ba and bc are the anodic and cathodic Tafel slopes. The basis for this equation lies in the mixed potential theory proposed by Wagner and Traud in 1938. This paper (C. Wagner and W. Traud, "On the Interpretation of Corrosion Processes Through Superposition of Electrochemical Partial Processes and on the Potential of Mixed Electrodes, Z. Elektrochem. Ang. Physik. Chemie, Vol. 44, p. 391, 1938) has recently appeared in a translation by F. Mansfeld (F. Mansfeld, Corrosion, Vol. 62, p. 843, 2006).

Mixed potential theory forms the basis for the Stern-Geary equation that is used in the polarization resistance technique M. Stern and A. L. Geary, "Electrochemical Polarization, A Theoretical Analysis of the Shape of the Polarization Curves", J. Electrochem. Soc., Vol. 104, p. 56, 1957). The corrosion current can be related to the Tafel slopes by:

                                                                   (3)

No assumptions are needed to derive equation (3) beyond those for validity of equation (2). The derivation of equation (3) is completely mathematical. The assumption of linearity between voltage and current is not needed (F. Mansfeld and K. B. Oldham, Corrosion Science, Vol. 11, p. 787 (1971)). Substituting equation (3) into equation (2) enables Tafel slopes and the polarization resistance to be extracted from a curve-fitting of equation (2) to the actual data.

As shown in this figure the polarization resistance Rp is the reciprocal of the slope of the polarization curve at the corrosion potential when plotted with current density on the ordinate and voltage on the abscissa. The polarization resistance is inversely proportional to the corrosion current density which can be transformed to a corrosion or penetration rate for uniform corrosion. From equation (3), the information that would be needed to estimate the corrosion rate are values of the two Tafel slopes and the polarization resistance, all measured at the corrosion potential. The value of the technique lies in the fact that in many instances, the method of making the measurement does not interfere with the quantities being measured as long as the polarization is in the vicinity of the corrosion potential (about ± 30 mV or less) and the measurement can be made very quickly, usually in a matter of minutes. An example of a violation of this condition is provided elsewhere in this tutorial. Notice also that in the above figure, the curve is not linear in the vicinity of the corrosion potential. In addition, a polarization curve is symmetrical in the vicinity of the corrosion potential only when the two Tafel slopes are equal. Obtaining a good estimate of the polarization resistance can sometimes be much easier than obtaining good estimates for the Tafel slopes. When that issue occurs one can still estimate the corrosion current (corrosion rate) by rewriting equation (3) as

                                                                   (4)

and by assuming that B lies between about 10 and 30 mV (often about 15 to 25 mV).

Implicit Assumptions

Using equation (3) to quantify the corrosion process and estimate corrosion rates from a polarization curve such as that in the figure requires assumptions as summarized below.
  1. The reaction rate (corrosion current) can be expressed as being proportional to the exponential of the voltage offset from the corrosion potential for one oxidation (anodic) and one reduction (cathodic) reaction. If this assumption is not fulfilled, equation (1) has to be modified to account for all of the reactions that affect corrosion.
  2. Uncompensated resistance in the electrolyte is either absent or is much smaller than the polarization resistance. The resistance estimated by the polarization resistance technique contains all contributions to the total resistance. For example, most electrochemical systems involving charge transfer across an interface have both a polarization resistance Rp and an uncompensated solution resistance Rs. The polarization resistance as measured by this technique is equal to the sum of the actual polarization resistance and the uncompensated solution resistance,   . The current interrupt technique can sometimes be used effectively to correct for the uncompensated resistance. Most modern potentiostats have that capability.
  3. For the full form of equation (3) to be used, mass transfer cannot be the controlling or rate limiting step and both the anodic and cathodic reactions must be under activation control. Otherwise, the Tafel slope corresponding to the mass transfer controlled process is infinite. For example, if the process is under cathodic mass transfer control, the proportionality constant between Rp and icorr becomes ba/2.303. The technique can still, in principle, be used to estimate corrosion rates under these circumstances. In practice, a non-linear regression of the data versus the combined equations (2) and (3) should result in an extremely large Tafel slope for the sub-process under mass transfer control.
  4. The corrosion potential does not lie close to the reversible potentials for the oxidation and reduction reactions. Being 25 mV or so from the reversible potential is often sufficient to allow equation (2) to be valid.
  5. To estimate the rate of uniform corrosion from the polarization resistance, each reacting site across the entire electrode surface is assumed to function simultaneously as a cathode and an anode. The anodic and cathodic sub-reactions do not occur on different sites. This assumption is implicit in Mixed Potential Theory. In the extreme, if separated anodes and cathodes exist on the surface corrosion would be localized on the surface (e.g. pits) and the corrosion rate calculated using equations (2) and (3) would not be the rate of uniform corrosion. Note that the method might be used as a sensitive detector of such corrosion if such localized attack is severe. Success depends on how the experimental apparatus is used and resulting curve is analyzed. That application is beyond the scope of this discussion.
  6. No additional electrochemical reactions are occurring to interfere with the current density versus voltage curve.
Assessing how well these assumptions are fulfilled requires some knowledge of the corrosion process. The polarization resistance technique like all electrochemical techniques cannot be used blindly. Fulfilling the above assumptions means that using the polarization resistance technique to estimate the corrosion rate is valid for that corrosion process. Many practical systems are often poorly characterized so assessing how well these criteria are fulfilled can be difficult. Some degree of imprecision must be associated with the estimated corrosion rate under these conditions. Additional sources of error can arise when the technique is applied in practice.


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David C. Silverman, Ph.D. - Primary Consultant
E-Mail:     dcsilverman@argentumsolutions.com
Phone:     314-576-3586
Fax:         314-754-9825
Address:   The Argentum House
                14314 Strawbridge Ct.
                Chesterfield, MO 63017